A fluid line support system includes a fluid line and a collet having an insertion end and a thickened portion having a biased end. A fluid valve has a valve aperture that receives the insertion end of the collet. A collet securing device has a fluid line portion that engages the wall of the fluid line, wherein at least the fluid line portion encircles the wall and is slidably engaged with the wall to define a loose position and a securing position. A collet portion of the collet securing device engages the retaining portion of the fluid valve when in the securing position. When in the securing position, the fluid line portion engages the biased end of the collet, wherein the fluid line and collet portions bias the retaining portion and biased end toward one another such that the insertion end is positioned at a final insertion depth.